Assume the random variable X has distribution X ~ Bin(9,0.5) and let Y = (-1)x. 1....

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Assume the random variable X has distribution X ~ Bin(9,0.5) and let Y = (-1)x. 1. Derive the probability mass function of Y. 2. Derive the mean of Y 3. Derive the variance of Y.

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Answer 1

Answer #1

Let's make table in excel:

From this table Y takes only two values as -1 and 1 The probability mass function of Y is as follows: P(x) 1 0.001953 1 0.017578 1 0.070313 1 0.164063 1 0.246094 10.246094 1 0.164063 1 0.070313 1 0.017578 1 0.001953 p(y) 0.5 0.5 6 4 0.5 0.5 y*p(y)p(x)*(y - mean)A2 0.5 0.5 0.5 0.5 0 10 12

b) Therefore mean of Y is 0

c) and variance of Y is 1

The formulae used on the above excel-sheet are as follows:

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Answer 2

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Assume the random variable X has distribution X ~ Bin(9,0.5) and let Y = (-1)x. 1....

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Assume the random variable X has distribution X ~ Bin(9,0.5) and let Y = (-1)x. 1....

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